The Kaufman Assessment Battery for Children is designed to measure achievement and intelligence with a special emphasis on nonverbal intelligence. Its global measures, such as its Sequential...

The Kaufman Assessment Battery for Children is designed to measure achievement and intelligence with a special emphasis on nonverbal intelligence. Its global measures, such as its Sequential Processing score, are scaled to have a mean of 100 and a standard deviation of 15. Assume that the Sequential Processing score has a normal distribution.

(a) Find a value such that divides the children with the highest 10% of the scores from those with the lower 90%.

(b) What proportion of children will have Sequential Processing scores between 90 and 110?

(c) In a sample of 20 children, what is the probability the sample mean will differ from the population mean by more than 3 points (either positive or negative)?